In an isosceles trapezoid, the sum of the bases is equal to the sum of the sides, the perimeter is 32 cm.

univerkov | December 28, 2020 | education

In an isosceles trapezoid, the sum of the bases is equal to the sum of the sides, the perimeter is 32 cm. Find the side of the trapezoid.

Since, by condition, the sum of the lengths of the bases is equal to the sum of the sides, then (AB + СD) = (BC + АD).
The perimeter of the trapezoid is: Ravsd = (AB + BC + СD + АD), then:
Ravsd = (AB + СВ + AB + СD) = 2 * (AB + СD).
Since the trapezoid is isosceles, then AB = СD, then Ravsd = 4 * AB = 32.
AB = 32/4 = 8 cm.
Answer: The side of the trapezoid is 8 cm.

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